Let f be a function so that (below). Which must be true?I. f is continuous...
Let f be a function so that (below). Which must be true? I. f is continuous at x=2 II. f is differentiable at x=2 III. The derivative of f is continuous at x=2 (A) I (B) II (C) I and II (D) I and III (E) II and III
Answer & Explanation
Beginner2023-03-14Added 3 answers
(C) Explanation: Noting that a function is differentiable at a point if
the given information effectively is that is differentiable at and that .Now, looking at the statements: I: True A function's differentiability at a point implies its continuity at that point. II: True The given information matches the definition of differentiability at . III: False The derivative of a function is not necessarily continuous, a classic example being , which is differentiable at , but whose derivative has a discontinuity at .
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